Appendix A. Modification of the torus translation method to test for habitat associations.
We made two major modifications to the torus-translation method to accommodate unique characteristics of our data set. First, our plots are square, permitting eight translated habitat maps rather than the four originally described by Harms et al. (2001) for their rectangular plot. Our four supplementary maps correspond to 90º and 270º rotations and their mirror images of the original map. The second modification we made was because we used multiple plots rather than the single plot described by Harms et al. (2001). We calculated relative densities in all plots simultaneously and weighted the contribution from each plot to the final test statistic by the density of a species in each plot, as:
where ni,j,p is the number of stems of species i in habitat j in plot p, and dots represent the sum of a given index. This calculated test statistic (for the true map) was then compared to the distribution of the test statistic generated from the torus-translated permutations. Copies of the modifications to the R-language code are available from the corresponding author upon request.
For trees, complete inventories of all species were conducted throughout the study period; therefore, any individual of the eight focal species that recruited to 10 cm DBH during the study period could be contrasted with the absolute density of all species (Harms et al. 2001). For this data set we divided our square 6.25 ha plots into 10 × 10-m quadrats. Each quadrat was then assigned to seasonally-flooded or terra firme forest, based on whether the majority of stems in the quadrat were located in the GIS database layer defined by seasonally-flooded forest, criteria of periodic inundation to soil surface and a water table never descending below 1 m (Salvado 2002). This procedure resulted in 4999 unique torus-translated habitat maps in addition to the original untranslated map.
For the sapling data set, three further modifications were necessary. First, we treated each subplot as a grid cell, and we thus treated an 8 × 8 grid, resulting in 511 torus-translated habitat maps. Second, we analyzed only the five plots within which the subplots covered both seasonally-flooded and terra firme forest. Third, absolute density (number of stems of all species in each plot) was only available for the 2005 inventory. We thus report results only for those individuals present in 2005, as this is most consistent with the approach used for trees.
LITERATURE CITED
Harms, K. E., R. Condit, S. P. Hubbell, and R. B. Foster. 2001. Habitat associations of trees and shrubs in a 50-ha neotropical forest plot. Journal of Ecology 89:947–959.
Salvado, A. 2002. Étude des relations entre sol et végétation en forêt tropicale humide : comparaison de la dynamique forestière selon les profondeurs de nappe en saison sèche (Bas fonds vs Sol drainé) et étude du comportement de la nappe en saison humide. Mémoire de DEA de Biologie Forestière, ENGREF, Nancy (France).